Good points there.
Also, the area of the Persian Empire is a continguous (and large) landmass, even though very variable in climate and landscape. The Greek motherland OTOH practically forces its inhabitants to rely on infantry warfare, because fertile plains, while they exist, are limited in extension and have to be utilized for agriculture of all kinds (and it's phantastic to see what you can grow in places like the Eurotas valley or the Argive plain - basically everything, except rice). Not much space for horse herds of sufficient quality or quantity there. The mountains are either forested or used for other livestock or wine, olives etc (curiously, nowadays, most of them are covered with maquis or garrigue. Probably a result of over-exploitation). Also, for most regions in Greece, ships are a much faster and more efficient means of transportation than horses.
Furthermore, the formation of small (city) states* is favoured by the Greek topography, and heavy infantry is a typical military element of city states.
*Polis doesn't necessarily indicate a city.
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